Exhibit

Exhibit 32.1

Certification Pursuant to 18 U.S.C. Sec. 1350

In connection with the filing by Tremont Mortgage Trust (the “Company”) of the Quarterly Report on Form 10-Q for the period ended June 30, 2020 (the “Report”), each of the undersigned hereby certifies, to the best of his knowledge:


1)	The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and


2)	The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.



/s/ G. Douglas Lanois		/s/ David M. Blackman
G. Douglas Lanois Chief Financial Officer and Treasurer		David M. Blackman President and Chief Executive Officer

Date: August 4, 2020